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To adapt or to confirm: what is the question?

This outline discusses dose-ranging studies, adaptive model-based designs, and statistical operational characteristics. It explores the goal of efficient learning about dose response and improved decision making on dose selection. The focus is on evaluating alternative designs and methods through simulation studies. Presented by Vlad Dragalin at the PhRMA ADRS Working Group in St. Petersburg, Russia.

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To adapt or to confirm: what is the question?

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  1. To adapt or to confirm: what is the question? Vlad Dragalin Wyeth Research

  2. Outline • Dose-ranging studies • Adaptive model-based designs • Statistical Operational Characteristics • Conclusion V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  3. PhRMA ADRS Working Group • One of 10 PISC WGs formed 4 years ago • Overall goal: • investigate and develop designs and methods for efficientlearning about DR • more accurate and faster decision making on dose selection and improved labeling • How: • evaluate statistical operational characteristics of alternative designs and methods via comprehensive simulation studies • Focus: • adaptive and model-based • dose-ranging designs and methods V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  4. ADRS WG: Members Co-Chairs: José Pinheiro and Rick Sax Original Members: Björn Bornkamp, Frank Bretz, Alex Dmitrienko, Greg Enas, Brenda Gaydos, Chyi-Hung Hsu, Franz König, Michael Krams, Qing Liu, Beat Neuenschwander Tom Parke, Amit Roy, Frank Shen New Members: Zoran Antonijevic Vlad Dragalin Parvin Fardipour Marc Gastonguay Bill Gillespie Frank Miller Krishna Padmanabhan Inna Perevozskaya Nitin Patel Jonathan Smith V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  5. Dose-Ranging Studies • The overall goal of dose-ranging studies is to establish the existence, nature and extent of dose effect: • Detecting DR: evaluate if there is evidence of activity associated with the drug, represented by a change in clinical response resulting from a change in dose (PoC); • Identifying clinical relevance: if PoC is established, determine if a pre-defined clinically relevant response (compared to the placebo response) can be obtained within the observed dose range; • Selecting a target dose: when the previous goal is met, select the dose to be brought into the confirmatory phase, the so-called target dose; • Estimating the dose response: finally, estimate the dose-response profile within the observed dose range. V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  6. Simulation Study: Complete Summary V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  7. New Adaptive Designs • AMCP-Mod–Adaptive MCP-Mod approach combining multiple comparisons and modeling (Bornkamp, Bretz, Pinheiro) • DCoD– D-optimal followed by a c-optimal design based on sigmoid Emax model (Dragalin, Padmanabhan) • IntR– Bayesian design minimizing average variance of all LS-estimates for “interesting part” of dose-response curve (Miller) • MultObj – Multi-objective optimal design incorporating 2nd order moments and based on inverse quadratic model (Smith) • T-Stat – Dose-adaptive design based on t-statistics (Patel, Perevozskaya) V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  8. AMCP-Mod Design V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  9. Adaptive MCP-Mod Design • Extension to a response-adaptive version of the MCP-Mod methodology using • optimal design theory to allocate new cohorts of patients • posterior model probabilities and posterior parameter estimates to update initial guesses • AMCP-Mod Before Trial Start • Select the candidate models (two logistic and one beta models) • Select “best guesses” for , m = 1, . . . ,M • Choose prior model probabilities p(Mm) • Choose prior for V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  10. Adaptive MCP-Mod Design at IA V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  11. Adaptive MCP-Mod Design at Trial End • Calculate optimal contrasts and critical value using MCP • Select one of the significant models for dose-response and MED estimation • Fit dose-response model and estimate MED • Bayesian model is only used for updating the design; the classical MCP-Mod procedure is wrapped around this. V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  12. DCoD: Adaptive Dc-optimal Design • Working Model Sigmoid Emax model (4 parameter logistic) Dragalin et al V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  13. Sigmoid Emax Fit V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  14. D- and c-optimal Designs • D-optimal design (LDoD) minimizes • c-optimal (LcoD) minimizes • Kiefer-Wolfowitz Equivalence Theorem V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  15. Sigmoid Emax Scenario V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  16. Emax Scenario V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  17. Emax Low Scenario V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  18. Umbrella Scenario V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  19. Adaptive Dc-optimal Design • For 2 adaptations: • 1/3rd of the subjects allocated according to a fixed 5-dose design • Parameters are estimated –> next 1/3rd allocated according to augmented LDoD • Parameters are re-estimated –> final 1/3rd allocated according to augmented LcoD V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  20. IntR Design • Estimation of the interesting part of the dose-response curve • Working model: sigmoid Emax • Inference based on LS estimates from this Emax-sigmoid model • Minimize average variance of all LS-estimates for f(x) - f(0) with xδ<x<8. xδ is dose with effect 1 compared to placebo • “Detecting Dose-Response”: trend test used to test null hypothesis of flat dose-response xδ V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  21. IntR Design V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  22. MULTOBJ Design • Primary focus within MULTOBJ criterion is MED estimation • Lower weighted components also included related to POC and EDp (for a range of p’s) • Additional low wt. components related to nonlinearity • Weights chosen to reflect importance of component criteria • All of above based on 2nd order moments V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  23. MULTOBJ Design • MULTOBJcriterion is essentially an extended form of S-optimality but incorporating 2nd order moments and with MSE in place of variances • Working Model: Non-Monotonic 4 parameter Inverse Quadratic model V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  24. T-statistic design • Non-parametric design adaptive approach • Concentrates dose allocations around the dose with target (pbo-adjusted) response level • Patients are randomized sequentially in cohorts of fixed size; all assigned to the same dose or pbo (e.g. 3:1) • Dose selection is adaptive and driven by the value of t-statistic at the last dose studied (Ti): • Escalate to xi+1 if Ti • Stay at xi if -<Ti≤ • De-escalate to xi-1 if Ti ≤- • Where x1=pbo, x2,…, xK are active doses, • xiis current dose (at the time of IA), • Tiis standardized pbo-adjusted mean response at dose xi •  is a design parameter Ivanova A., Bolognese JA, Perevozskaya I. Adaptive dose-finding based on t-statistic in dose-response trial. Stat in Medicine, 2008; 27:1581-1592 V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  25. Simulation Study: Assumptions • Doses: • 9 doses: {0,1,2,3,4,5,6,7,8} • 5 doses: {0,2,4,6,8} • Endpoint: change from baseline in VAS score • Clinically meaningful difference: –1.3 • Variance: 4.5 • Sample Size: 250 • Number of adaptations: 0,1,2,4,9 • Total of 56 combinations V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  26. Simulation Scenarios • Linear: y = -(1.65/8) d +  • Umbrella: y = -(1.65/3)d + (1.65/36)d2 +  • Sigmoid Emax: y = -1.70 d5/(45 + d5) +  • Emax: y = -1.81 d/(0.79 + d) +  • Emax low: y = -1.14 d/(0.79 + d) +  • Explicit: y = {0, -1.29, -1.35, -1.42, -1.5, -1.6, -1.63, -1.65, -1.65} +  • Flat: y = . V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  27. Simulation Scenarios V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  28. Performance metrics • Probability of detecting dose response: Pr(DR) • Probability of identifying clinically relevant dose: Pr(dose) • Target Dose selection • Distribution of selected doses • Summary statistics (mean and standard deviation) for percentage difference from target • pDiff = 100( d - dtarg)/dtarg • Dose Response estimation: • summary statistics for average prediction error • (PE): 100|DRest - DR|/DR • Subject Allocation pattern V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  29. Detecting Dose-Response: type I error V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  30. Detecting D-R: power for 9 doses V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  31. Identifying clinically-relevant dose: flat D-R V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  32. Identifying clinically-relevant dose V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  33. Selecting Target Dose:9 doses V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  34. Selecting a target dose: distribution V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  35. Estimating D-R curve V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  36. Summary and Conclusions • Detecting DR is considerably easier than estimating it • Current sample sizes used for D-R studies are inadequate for dose selection and D-R estimation • Adaptive methods lead to gain in power to detect DR + precision of target dose selection + DR estimation compared to traditional ANOVA design V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  37. Summary and Conclusions (cont.) • None of the designs was a uniformly superior to the others • All 5 designs performed well with respect to achieving specific objective they were designed for: • IntR, did well for DR estimation • AMCPMod, t-test: did well for dose selection • MULTOB and DcoD: did well for both objectives • The appeal of a particular design will depend on • the specific goal of the trial • and the set of plausible DR scenarios, because the latter affects relative performance of the designs V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

  38. Summary and Conclusions (cont.) • Due to complexity of the designs, operating characteristics can be assessed only via simulations during the DR trial planning stage • Need software which is sufficiently flexible, comprehensive and extensible to allow in-depth exploration of various methods to determine design most appropriate for the study • We investigated impact of only one component of AD: allocation rule and adaptation based on efficacy endpoint only • The approach can be extended to examine other sources of “adaptivity”: • sampling rule, • early stopping for futility/efficacy, • information-driven SS determination, • using early data through longitudinal modeling V. Dragalin | To adapt or to confirm: what is the question?| St. Petersburg, Russia

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